Question

The circumference of the base of a cylinder is 176cm and its height is 30cm. find the volume of the cylinder.

Answer 1

Hint: To find the volume of the cylinder first we should find the radius. From the circumference formula we find the radius. Then we find the volume by substituting radius. The formula for volume of the cylinder is $V = \pi {r^2}h$ where r is the radius and h is the height.

Complete Step by Step Solution:
The objective of the problem is to find the volume of the given cylinder.
To find volume we need height and radius. Height is given in the question we need to find radius to find radius we should find the circumference.
Given that,
Circumference of the base of the cylinder = 176cm.
Height (h)=30cm
The formula for circumference of the base of the cylinder $ = 2\pi r$
But it is given that circumference of the base of the cylinder is 176cm
Therefore , $2\pi r = 176$
On dividing with two on both sides we get
$
   \Rightarrow \dfrac{{2\pi r}}{2} = \dfrac{{176}}{2} \\
   \Rightarrow \pi r = 88 \\
 $
Taking $\pi $ as $\dfrac{{22}}{7}$ we get
$ \Rightarrow \dfrac{{22}}{7}r = 88$
By sending $\dfrac{{22}}{7}$ to right side we get the reciprocal of $\dfrac{{22}}{7}$ which is $\dfrac{7}{{22}}$
$
   \Rightarrow r = 88 \times \dfrac{7}{{22}} \\
   \Rightarrow r = 4 \times 7 \\
   \Rightarrow r = 28 \\
 $
Therefore , the radius(r) is 28cm.
Now we have to find the volume of the cylinder.
The volume of the cylinder (V)$ = \pi {r^2}h$ , where r is the radius and h is the height of the cylinder.
We have, the radius of the base of the cylinder(r)=28cm
Height of the cylinder(h)$ = 30cm$.
Now substitute height and radius in volume. We get ,
 $
  V = \pi {r^2}h \\
  \,\,\,\,\, = \pi {\left( {28} \right)^2}\left( {30} \right) \\
 $
Taking $\pi $ as $\dfrac{{22}}{7}$ and on multiplication we get,
   $
   = \dfrac{{22}}{7} \times 28 \times 28 \times 30 \\
   = 22 \times 4 \times 28 \times 30 \\
   = 73,920c{m^3} \\
 $

Therefore , the volume of the cylinder is $73920\,c{m^3}$.

Note:
It is easier to take the value of pi as 22/1 than in decimal values. The decimal value of pi is 3.14 approximately. The bases of the cylinder are always congruent and parallel. If the bases are in circular shape then it is called a right circular cylinder and if the bases are in elliptical shape then it is called an elliptical cylinder.